It wasn't just Anakin trying to protect himself from punishment - he was making sure Obi-Wan didn't have consequences for tolerating Anakin's rule breaking.

"I wasn't trying to hid from you. I was just cold." Coruscant felt cold to him. It always had and Anakin couldn't understand why. Tatooine got cold at night, deadly so. Coruscant didn't have the huge temperature swings, and yet. He always noticed the cold here.